A244866 - OEIS

%I #11 Nov 09 2022 13:36:22

%S 1,18,114,438,1263,3024,6356,12132,21501,35926,57222,87594,129675,

%T 186564,261864,359720,484857,642618,839002,1080702,1375143,1730520,

%U 2155836,2660940,3256565,3954366,4766958,5707954,6792003,8034828,9453264,11065296,12890097,14948066,17260866,19851462,22744159

%N Let G denote the 7-node, 12-edge graph formed from a hexagon with main diagonals drawn and a node at the center; a(n) = number of magic labelings of G with magic sum 2n.

%H Colin Barker, <a href="/A244866/b244866.txt">Table of n, a(n) for n = 0..1000</a>

%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F G.f.: (1 + 12*x + 21*x^2 + 4*x^3) / (1 - x)^6.

%F From _Colin Barker_, Jan 11 2017: (Start)

%F a(n) = (n + 1)*(n + 2)*(19*n^3 + 63*n^2 + 68*n + 30) / 60.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.

%F (End)

%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,18,114,438,1263,3024},40] (* _Harvey P. Dale_, Nov 09 2022 *)

%o (PARI) Vec((1 + 12*x + 21*x^2 + 4*x^3) / (1 - x)^6 + O(x^40)) \\ _Colin Barker_, Jan 11 2017

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jul 07 2014